If the major i want to study is not included in college majors,,,

I wanna study Engineering but a community college i wanna go doesn’t have that major.
i need the transferable credits of math and science mainly to transfer to 4-year univ.
in this case, if i choose my major one of math and science(especially physics), can i transfer to Engineering Department?

You don’t have to major in a particular subject at a community college in order to transfer into that major. You just have to have the right courses that the transferring-into institution wants to see for students transferring into a specific major. Having said that, however, in order to transfer into an Engineering program as a Junior, you will need to have taken a number of Engineering courses. If your community college doesn’t have any Engineering courses, then you will not be able to transfer into an Engineering program as a rising Junior.

At my community college, students need to take the following in order to be ready to transfer into Bachelor’s degree Engineering programs: Calculus, up through multivariate Calculus (i.e. usually 3 semesters or 4 quarters of calc), Differential Equations, Linear Algebra, a year of calculus-based Physics, one or two semesters of General Chemistry, depending on the Engineering discipline, General Ed courses ( one or two each of Humanities and Social Sciences), Computer Programming (Java or C++, depending on Engineering discipline). All of this will take close to 2 years to complete. However, you should also have some Engineering courses that 4-year students take as Freshmen or Sophomores: Intro to Engineering, Statics, Dynamics, Strength of Materials, Circuits, Thermodynamics.